The present invention relates to an acoustic transfer function simulating method which is used with an acoustic echo canceller, a sound image localization simulator, an acoustic device which requires the simulation of an acoustic transfer function for dereverberation, active noise control, etc., and an acoustic signal processor, for simulating the transmission characteristics of a sound between a source and a receiver. The invention also pertains to a simulator utilizing the above-mentioned method.
The acoustic transfer function simulating method is a method which simulates, by use of a digital filter, the transmission characteristics of a sound between a source and a receiver placed in an acoustic system (e.g. a sound field). In this specification, the transfer function of the acoustic system is expressed by a true acoustic transfer function H(z), and the transfer function that is simulated by the acoustic transfer function simulating method will hereinafter be referred to as a simulation transfer function H'(z). Incidentally, the following description will be given on the assumption that signals are all discrete-time signals, but in the case of continuous-time signals, too, discussions on the discrete-time signals are equally applicable. In the discrete-time signal its time domain is expressed by, for example, x(t) using an integer parameter t representing discrete time, and its frequency domain by X(z) using a z-transform. Furthermore, an A/D converter and a D/A converter which are used, as required, in the acoustic transfer function simulator described hereinbelow are self-evident, and hence no description will be given of them, for the sake of brevity.
FIG. 1A is a schematic diagram for explaining the true acoustic transfer function H(z) in a room. In the case where a sound source (for example, a loudspeaker) 12 and a receiver (for instance, a microphone) 13 are disposed in a sound field 11 and a signal X(z) is applied to an input end 14 to output the signal X(z) from the sound source 12, the signal X(z) will reach the receiver 13 under the influence of the true acoustic transfer function H(z) in the room 11. A signal Y(z) received by the receiver 13 is output via an output end 15. The true acoustic transfer function H(z) describes the input-output relationship of the output signal Y(z) at the output end 15 to the input signal X(z) at the input end 14, and it is expressed as follows: EQU H(z)=Y(z)/X(z) (1)
The true acoustic transfer function H(z) differs with different positions of the sound source 12 and the receiver 13 even in the same room.
The simulation of the acoustic transfer function is to simulate the true acoustic transfer function H(z) which is the above-mentioned signal input-output relationship, by use of an electrical filter or the like. FIG. 1B is a schematic diagram for explaining it. The transfer function of a filter 16 is the simulated transfer function H'(z). In the case where the simulated transfer function H'(z) is equal to the true acoustic transfer function H(z) in FIG. 1A, when applying the same signal as that X(z) at the input end 14 in FIG. 1A to an input end 17 of the filter 16, an output signal Y'(z), which is provided an output end 18 via the filter 16 having the simulation transfer function H'(z), becomes equal to the signal Y(z) at the output end 15 in FIG. 1A.
The acoustic transfer function simulating method that has been employed most widely in the past is a method of simulating the true acoustic transfer function H(z) by a model called moving average model (MA model) or all zero model. In the case of utilizing the MA model, the simulation transfer function H'.sub.MA (z) is expressed as follows: ##EQU1## A filter embodying the transfer function expressed by Eq. (2) will hereinafter be referred to as an MA filter. Further, h'(n) in Eq. (2) will hereinafter be referred to as MA coefficients and N an MA filter order. It is well-known in the art that the MA filter could be implemented through utilization of an FIR (Finite Impulse Response) filter.
It is well-known in the art that the input-output relationship in the time domain in the case of using the MA filter is expressed using the MA coefficients h'.sub.n as follows: ##EQU2## where x(t) is the input signal and y'(t) the output signal.
FIG. 1C is a schematic diagram for explaining the acoustic transfer function simulating method utilizing the MA filter. The MA filter 19 has the MA coefficients h'(n) as its filter coefficients. Letting an impulse response of the true acoustic transfer function H(z) be represented by h(t) and letting the MA filter coefficients h'.sub.n =h(n), a simulation with a minimum error is achieved as is well-known in the art.
Incidentally, the simulation of the acoustic transfer function H(z) through use of the MA filter generally calls for the filter order corresponding to the reverberation time of a room, and hence has a shortcoming that the scale of the system used is large. Moreover, the true acoustic transfer function H(z) varies with the positions of the sound source and the receiver as referred to previously--this poses a problem that all MA filter coefficients have to be modified accordingly. For instance, in an acoustic echo canceller which has to estimate and simulate an unknown acoustic transfer function at high speed, it corresponds to the re-estimation of all the coefficients of the MA filter forming an estimated echo path, leading to serious problems such as impaired echo return loss enhancement (ERLE) by a change in the acoustic transfer function and slow convergence by the adaptation of all the MA filter coefficients.
Next, a description will be given of another conventional simulation method which performs simulation of the true acoustic transfer function by a model called autoregressive moving average model (ARMA model) or pole-zero model. In the case of utilizing the ARMA model, the simulation transfer function H'.sub.ARMA (z) is expressed as follows: ##EQU3## In the above, Q=Q.sub.1 +Q.sub.2. A filter which embodies the transfer function H'.sub.ARMA (z) expressed by Eq. (4) or (5) will hereinafter be referred to as an ARMA filter. Letting the denominators and the numerators in Eqs. (4) and (5) be represented by A'(z) and B'(z), respectively, a filter which embodies a transfer function expressed by B'(z) will hereinafter be referred to as a MA filter. Since B'(z) is expressed in the same form as that by Eq. (2) based on the afore-mentioned MA model, the both filters will hereinafter be referred to under the same name unless a confusion arises between them. Further, a filter which embodies a transfer function expressed by 1/A'(z) will hereinafter be referred to as an AR filter. Moreover, filters which embody transfer functions A'(z) and (1-A'(z)) will also be referred to as AR filters, but they will be called an A'(z) type AR filter and a (1-A'(z)) type AR filter, respectively. a'.sub.n and b' .sub.n in Eq. (4) will be called AR coefficients and MA coefficients, respectively, and these coefficients, put together, will be called ARMA coefficients. P and Q in Eq. (4) will hereinafter be called an AR filter order and an MA filter order, respectively. Eq. (5) represents, in factorized form, polynomials of the denominator and the numerator in Eq. (4), and Z.sub.e '.sub.i is called zero for making the transfer function H'.sub.ARMA (z) to zero, and Z.sub.p '.sub.i pole for making the transfer function H'.sub.ARMA (z) infinite. This ARMA filter can be realized through utilization of an IIR (infinite impulse response) filter.
As will be seen from the relationship between Eqs. (4) and (5), once the AR and MA coefficients which provide the polynomials in the denominators and the numerators are determined, factors of the polynomials are unequivocally determined; hence, it can be said that the poles and the zeros have a one-to-one correspondence with the AR coefficients and the MA coefficients, respectively. As is well-known in the art, the input-output relationship in the case of employing the ARMA filter can be expressed using the AR coefficients a'.sub.n and the MA coefficients b'.sub.n as follows: ##EQU4## where x(t) is the input signal and y'(t) the output signal.
Now, the simulation transfer function expressed by Eqs. (4) and (5) can be expressed as follows: EQU H'.sub.ARMA (z)=B'(z)/A'(z)=B'(z){1/A'(z)}
FIG. 1D shows an example of an arrangement for simulating the transfer function by use of the ARMA filter, which is a series-connection of an AR filter 21 having the 1/A'(z) characteristics and an MA filter 22 having the B'(z) characteristics. The AR filter 21 and the MA filter 22 may also be exchanged in position.
Next, a description will be given of two typical methods for obtaining the ARMA coefficients a'.sub.n and b'.sub.n necessary for a good simulation of the true acoustic transfer function. A first one of them is a method for obtaining the ARMA coefficients from values of zeros and poles, and a second method is a method of calculating the ARMA coefficients from the input-output relationship through use of a normal equation (a Wiener-Hopf equation). The second method includes a method of determining the ARMA coefficients by solving the Wiener-Hopf equation through use of measured values of the output signal y(t) based on a given input signal x(t), and a method of similarly calculating the ARMA coefficients by solving the Wiener-Hopf equation by use of measured values of an impulse response which represents a temporal or time-varied input-output relationship between the input signal x(t) and the output signal y(t). (In the following description the calculation of the ARMA coefficients from the input-output relationship or the measured values of the impulse response will be called ARMA modeling.)
According to the first method, in the case where, letting the number of zeros, the number of poles, each zero in the z-plane and each pole in the z-plane be represented by Q, P, Z.sub.ei (i=1, 2, 3, . . . , Q) and Z.sub.pi (i=1, 2, 3, . . . , P), respectively, values of zeros and poles can be calculated on the basis of an acoustic theory or the like through utilization of geometrical and physical conditions of the sound field, such as its shape, dimensions, reflectivity, etc., these values are substituted into Eq. (5) to expand it to the form of Eq. (4), thereby determining the AR and MA coefficients a'.sub.n and b'.sub.n. In practice, however, it is only for very simple sound field that the values of zeros and poles can be calculated on the basis of the acoustic theory. In many cases it is difficult to obtain the values of zeros and poles through theoretical calculations alone.
According to the second method (ARMA modeling), for example, in the acoustic system 11 of FIG. 1A wherein the sound source 12 and the receiver 13 are disposed, the output signal y(t) from the receiver 13 is measured when the input signal x(t), for example, white noise of a "zero" average amplitude, is applied to the sound source 12. Let it be assumed, here, that the input-output relationship is described as shown in Eq. (6). The numbers of zeros and poles are predetermined, taking into account the transfer function to be simulated and the required simulation accuracy. Now, if the difference between a simulation output signal y'(t) of the ARMA filter and a true output signal y(t) becomes minimum in some sense, then it can be considered that an excellent simulation of the acoustic transfer function by use of the ARMA filter could be achieved. It is possible to employ a well-known method of solving the Wiener-Hopf equation for obtaining ARMA coefficients which minimize an expected values of a squared error, given by the following Eq. (7), between the simulation output signal y'(t) of the ARMA filter and the true output signal y(t): EQU e(t).sup.2 ={y(t)-y'(t)}.sup.2 ( 7)
Letting an expected value operator be represented by E[.], the expected value .epsilon. of the squared error in Eq. (7) can be expressed, by use of Eq. (6), as follows: ##EQU5## The expected value .epsilon. of the square error becomes minimum when all derivatives, obtained by partially differentiating the expected value .epsilon. with respect to the coefficients a'.sub.n (n=1, 2, 3, . . . , P) and b'.sub.n (n=0, 1, 2, 3, . . . , Q), become zeros at the same time. Since in Eq. (8) the value of the output signal y'(t) cannot be obtained before the values of the coefficients a'.sub.n and b'.sub.n are determined, however, the expected value of the square error is minimized replacing the simulation output signal y'(t) with the true output signal y(t). This is an ordinary method called "equation error method."
Derivatives of the coefficients a'.sub.n and b'.sub.n in Eq. (8) become as follows: ##EQU6## By solving the simultaneous equations (normal equations) so that the derivatives become zero at the same time, values of the ARMA coefficients a'.sub.n and b'.sub.n can be obtained. In this instance, the expected value operation cannot be done infinitely, and hence is replaced by an average for a sufficiently long finite period of time.
RLS, LMS and normalized LMS methods which are adaptive algorithms, as well as the above-described method involving normal equations can be used to determine the ARMA coefficients for the simulation with a minimum squared error.
Next, a description will be given of another second method according to which an impulse signal is applied as the input signal x(t) to the sound source, the response signals are measured and then the ARMA coefficients are determined. The impulse response is a signal which is observed in the receiver when a unit impulse .delta.(t) is applied as the input signal x(t) to the sound source. The unit impulse .delta.(t) takes values 1 and 0 when t=0 and t.noteq.0, respectively. The MA model utilizes the impulse response intact for simulating the acoustic transfer function, but since the ARMA model is used to simulate the acoustic transfer function in this case, the ARMA coefficients are determined on the basis of the measured impulse response.
Once the impulse response of the acoustic system is found, the input-output relationship, i.e. the relationship between the input signal x(t) to the sound source and the observed signal y(t) in the receiver can be defined, and hence it is possible to employ Eq. (9) which is basically applicable to any given input signal x(t). Substituting the unit impulse .delta.(t) for x(t) and the time series h(t) of the measured impulse response for y(t) in Eq. (9) gives ##EQU7## By solving the simultaneous equations (i.e. normal equations) so that the derivatives become zero at the same time, values of the ARMA coefficients a'.sub.n and b'.sub.n can be obtained. The expected value operation with the operator E[.] in this instance is, for example, an averaging operation corresponding to the measured impulse response length which corresponds to L in Eq. (w).
The second conventional methods which simulate the acoustic transfer function by use of the ARMA filter described above are advantageous in that the orders of filters used are lower than in the first conventional method using only the MA filter. In other words, the use of N in Eq. (w) and P and Q in Eq. (4) provides the relationship P+Q&lt;N, in general--this affords reduction of the computational load, and hence diminishes the scale of apparatus. With the second conventional methods, however, it is also necessary to change all ARMA coefficients when the positions of the sound source and the receiver are changed, as in the case of the first traditional method. Moreover, the method of adaptively estimating both of the AR and MA coefficients requires an adaptive algorithm which needs a large computational power for increasing the convergence speed to some extent, as compared with the method of estimating only the MA coefficients.
FIG. 2 is a block diagram schematically showing, as a first example of a conventional acoustic transfer function simulator, a conventional acoustic echo canceller (hereinafter referred to as an echo canceller) which employs an adaptive MA filter (i.e. an FIR filter) as disclosed in Japanese Patent Application Laid Open No. 220530/89, for example. In a hands-free telecommunication between remote stations via a network of transmission lines, such as a video teleconferencing service, a received input signal x(t) to an input terminal 23 from the far-end station is reproduced from a loudspeaker 24. On the other hand, the caller's speech is received by a microphone 25, from which it is sent out as a transmission signal to the remote or called station via a signal output terminal 26. The echo canceller is employed to prevent that the received input signal reproduced by the loudspeaker 24 is received by the microphone 25 and transmitted together with the transmission signal (that is, to prevent an acoustic echo).
To cancel such an acoustic echo, an acoustic transfer function simulation circuit 28 is formed using an adaptive MA filter 27, the acoustic transfer function H(z) between the loudspeaker 24 and the microphone 25 is simulated by the simulation circuit 28, and the received input signal x(t) at the input terminal 23 is applied to the acoustic transfer function simulation circuit 28 to create a simulated echo y'(t), which is used to cancel the acoustic echo y(t) received by the microphone 25 in a signal subtractor 29. Since the acoustic transfer function H(z) varies with a change in the position of the microphone 25, for instance, it is necessary to perform an adaptive estimation and simulation through use of the adaptive MA filter 27. That is, a square error between the simulated echo y'(t) at the output of the simulation circuit 28 and the acoustic echo y(t) received by the microphone 25 is obtained by the subtractor 29 and the coefficients of the MA filter 27 are adaptively calculated by a coefficient calculator 30 so that the square error may be minimized.
As mentioned previously, however, the echo canceller is defective in that the device scale become inevitably large because of large filter orders and that all filter coefficients must be changed with a variation in the acoustic transfer function.
FIG. 3 shows, as another example of the conventional acoustic echo canceller, the construction of an echo canceller employing a series-parallel type adaptive ARMA filter. In this instance, the output from the microphone 25 supplied with an acoustic output signal or acoustic echo is applied to an adaptive AR filter 31, the output of which is added by an adder 31A to the output of an adaptive MA filter 32, and the added output is provided as the simulated echo output to the subtractor 29. That is, the acoustic transfer function simulation circuit 28 is formed as a series-parallel type ARMA filter by the (1-A'(z)) type adaptive AR filter 31 which is series to the acoustic system 11 and the adaptive MA filter 32 which is parallel to the acoustic system 11. The ARMA filter is described as a means for obtaining the ARMA filter output when y'(t) on the right-hand side of Eq. (6) is replaced by y(t), and the AR filter 31 is formed by an AR filter having the (1-A'(z)) characteristics. The coefficients of the AR and MA filters 31 and 32 are adaptively calculated by coefficient calculators 30A and 30B so that the error of the subtractor 29 may be minimized. It is also possible to constitute an echo canceller by substituting the above-mentioned series-parallel type ARMA filter with a so-called parallel type ARMA filter, that is, by providing in parallel to the acoustic system an ARMA filter formed by a series-connection of an AR filter 33 having the 1/A'(z) characteristic and the MA filter 32 as shown in FIG. 4.
The circuit constructions utilizing such adaptive ARMA filters as shown in FIGS. 3 and 4 are advantageous over the circuit construction employing only the adaptive MA filter 27 shown in FIG. 2 in that the orders of the filters can be decreased or lowered, and hence the scale of calculation of the coefficients in the coefficient calculators 30A and 30B can be reduced. However, the algorithm for simultaneously estimating the MA and AR coefficients in real time is so complex that the above-noted echo cancellers are not put to practical use at present.
A second example of the conventional acoustic transfer function simulator, to which the present invention pertains, is a sound image localization simulator. The sound image localization simulator is a device which enables a listener to localize a sound image at a given position while the listener is listening through headphones. The principle of such a sound image localization simulator will be described with reference to FIG. 5. In FIG. 5, when the signal X(z) is applied to a loudspeaker 34, an acoustic signal therefrom reaches right and left ears of a listener 35 while being subjected to acoustic transmission characteristics H.sub.R (z,.theta.) and H.sub.L (z,.theta.) between the loudspeaker 34 and the listener's ears. In other words, the listener 35 listens to a signal H.sub.R (z,.theta.)X(z) by the right ear and a signal H.sub.L (z,.theta.)X(z) by the left ear. The acoustic transfer characteristics H.sub.R (z,.theta.) and H.sub.L (z,.theta.) are commonly referred to as head-related transfer functions (HRTFs), and the difference in hearing between the right and left ears, that is, the difference between H.sub.R and H.sub.L constitutes an important factor for humans to perceive the sound direction.
The sound image localization simulator simulates the acoustic transmission characteristics from the sound source to receivers 36R and 36L inserted in listener's external ears as shown in FIG. 5. Signals received by the receivers 36R and 36L in the listener's external ears are equivalent to sounds the listener listens with the eardrums. The sound image localization simulator can be implemented by inserting the receivers 36R and 36L in the external ears, measuring the head-related transfer functions H.sub.R (z,.theta.) and H.sub.L (z,.theta.) and reproducing the head-related transfer functions by use of a filter. In FIG. 5 the loudspeaker 34 is disposed in front of the listener 35 at an angle .theta. to the listener. Applying the signal X(z) from a head-related transfer function measuring device 37 to the loudspeaker 34, the acoustic signal from the loudspeaker 34 reaches the receivers 36R and 36L while being subjected to the acoustic transmission characteristics H.sub.R (z,.theta.) and H.sub.L (z,.theta.) between the loudspeaker 34 and the listener's ears as referred to above. The head-related transfer function measuring device 37 measures, for example, impulse responses h'.sub.R (n,.theta.) and h'.sub.L (n,.theta.) of head-related transfer functions H'.sub.R (z,.theta.) and H'.sub.L (z,.theta.). In this way, sets of impulse response h'.sub.R (n,.theta.) and h'.sub.L (n,.theta.) of the head-related transfer functions H'.sub.R (z,.theta.) and H'L.sub.( z,.theta.) are measured for a required number of different angles .theta.. The sets of the impulse responses thus measured are each stored in a memory 38 in correspondence with one of the angles .theta..
In the case of supplying a listener 35' with the signal X(z) from a sound source assumed to be disposed in the direction of a desired angle .theta. in FIG. 5, an angular signal represented by the same character .theta. is applied to an input terminal 39 together with the input signal X(z). The angular signal .theta. is applied as an address to the memory 38, from which is read out the set of impulse response h'.sub.R (n,.theta.) and h'.sub.L (n,.theta.) corresponding to the angle .theta.. The impulse responses thus read out are set as filter coefficients in filters 40R and 40L, to which the signal X(z) is applied. Consequently, the listener 35' listens to a signal Y'.sub.R (z,.theta.)=H'.sub.R (z,.theta.)X(z) by the right ear and a signal Y'.sub.L (z,.theta.)=H'.sub.L (z,.theta.)X(z) by the left ear through headphones 41R and 41L. If the simulated transfer functions are sufficiently accurate, then it holds that H'.sub. R .perspectiveto.H.sub.R and H'.sub.L .perspectiveto.H.sub.L, that is, Y'.sub.R .perspectiveto.Y.sub.R and Y'.sub.L .perspectiveto.Y.sub.L. This agrees with the listening condition described above in respect of FIG. 5, and the listener listening through the headphones 41R and 41L localizes the sound source in the direction of the angle .theta.. In other words, the simulation circuit 28 made up of the filters 40R and 40L simulates the head-related transfer functions. In the case of reading out of the memory 38 the impulse response h'.sub.R (n,.theta.) and h'.sub.L (n,.theta.) corresponding to the desired angle .theta., it is also possible to apply the angle .theta. from the outside by detecting, for example, the positional relationship between the sound source and the listener 35'.
The head-related transfer function described above appreciably varies with the direction .theta. of the sound source as a matter of course. To localize sound images in various directions, it is necessary to measure the head-related transfer function in a number of directions and store the measured data, and the storage of such a large amount of data measured constitutes an obstacle to the practical use of devices of this kind. That is, the formation of the filters 40A and 40L by the conventional acoustic transfer function simulating method poses a problem that the quantity of stored data on the acoustic transfer function is extremely large.
FIG. 6 shows a conventional dereverberator as a third example of the conventional acoustic transfer function simulator to which the present invention pertains. The signal X(z) emitted from the loudspeaker 24 disposed in the room 11 is influenced by transmission characteristics H.sub.1 (z) and H.sub.2 (z) of the room and received by receivers 25.sub.1 and 25.sub.2. The thus received signals are expressed by H.sub.1 (z)X(z) and H.sub.2 (z)X(z), respectively. The signal that is influenced by the acoustic transmission characteristics of the room is called "reverberant signal" and the object of the dereverberator is to restore or reconstruct the original signal X(z) from the received signal.
Heretofore there have been proposed a variety of dereverberators, and the device shown in FIG. 6 is based on a method disclosed in M. Miyoshi and Y. Kaneda, "Inverse filtering of room acoustics," IEEE Trans. on Acoust., Speech and Signal Proc., Vol. ASSP-36, No. 2, pp. 145-152, 1988. This method is based on the fact that if the acoustic transmission characteristics H.sub.1 (z) and H.sub.2 (z) are measurable and can be represented as the MA model, then MA filters G.sub.1 (z) and G.sub.2 (z) exist which satisfy the following equation: EQU G.sub.1 (z)H.sub.1 (z)+G.sub.2 (z)H.sub.2 (z)=1 (11)
With the Miyoshi et al arrangement, an acoustic transmission characteristics measuring part 44 applies a predetermined signal X(z) to the loudspeaker 24 and measures the transfer functions H.sub.1 (z) and H.sub.2 (z) from the signals received by the microphones 25.sub.1 and 25.sub.2. In a coefficient calculating part 45 the MA filter characteristics G.sub.1 (z) and G.sub.2 (z) which satisfy Eq. (11) are calculated using the transmission characteristics H.sub.1 (z) and H.sub.2 (z), and they are set in dereverberating MA filters 42.sub.1 and 42.sub.2. Thereafter, an arbitrary signal X(z) is applied to the loudspeaker 24, the resulting outputs of the receivers 25.sub.1 and 25.sub.2 are supplied to the MA filters 42.sub.1 and 42.sub.2 and their outputs are added by an 20 adder 43 to obtain the following output signal Y(z): ##EQU8## Thus, the dereverberated original signal X(z) is reconstructed. The filters 42.sub.1 and 42.sub.2 which have the transmission characteristics G.sub.1 (z) and G.sub.2 (z) serve as filters the characteristics of which are inverse from the transmission characteristics H.sub.1 (z) and H.sub.2 (z), and the filters 42.sub.1 and 42.sub.2 and the adder 43 constitutes the simulation circuit 28 which simulates reverberation-free transmission characteristics with respect to the acoustic system 11. The coefficients of the inverse filters 42.sub.1 and 42.sub.2 need not be changed from their initialized values unless the sound field in the room 11 changes, but they must be modified adaptively when the sound field is changed.
A difficulty in this method lies in that the computational load necessary for deriving the filter characteristics G.sub.1 (z) and G.sub.2 (z) from the transmission characteristics H.sub.1 (z) and H.sub.2 (z) in the coefficient calculating part 45, and the computational load in this case increases in proportion to the square of the order of the transmission characteristics H.sub.1 (z) and H.sub.2 (z) (corresponding to L in Eq. (2)).
FIG. 7 shows, as a fourth example of the conventional acoustic transfer function simulator to which the present invention pertains, a conventional active noise controller for indoor use disclosed in U.S. Pat. No. 4,683,590, for example. Noise radiated from a noise source 46 in the sound field 11 is collected by the receiver 25 near the noise source 46. The acoustic signal X(z) thus collected is phase inverted by a phase inverter 47 to provide a signal -X(z), which is applied to each of filters 48.sub.1 and 48.sub.2 of transmission characteristics C.sub.1 (z) and C.sub.2 (z). The outputs of the filters 48.sub.1 and 48.sub.2 are provided to secondary sound sources 24.sub.1 and 24.sub.2, respectively, from which they are output as control sounds. Observed at a control point P is the sum of three signals of a noise signal H.sub.0 (z)X(z) influenced by the room acoustic characteristics H.sub.0 (z), an output signal -H.sub.1 (z)C.sub.1 (z)X(z) of the secondary sound source 24.sub.1 influenced by the room acoustic Characteristics H.sub.1 (z) and an output signal -H.sub. 2 (z)C.sub.2 (z)X(z) of the secondary sound source 24.sub.2 influenced by the acoustic characteristics H.sub.2 (z) of the sound field. That is, the observed signal E(z) is expressed as follows: ##EQU9## At this time, filter coefficients C.sub.1 (z) and C.sub.2 (z) exist which satisfy the following equation, and consequently, the observed signal E(z) can be reduced to zero and noise control is thus effected. EQU H.sub.1 (z)C.sub.1 (z)+H.sub.2 (z)C.sub.2 (z)=H.sub.0 (z) (14)
To perform this, signals are sequentially applied from the acoustic transmission characteristics measuring part 44 to the secondary sound sources 24.sub.1 and 24.sub.2, acoustic signal from the noise source 46 and the secondary sound sources 24.sub.1 and 24.sub.2 are sequentially collected by a receiver or microphone 50 placed at the control point P and measured values of such input and output signals are used to calculate acoustic transmission characteristics H.sub.0 (z), H.sub.1 (z) and H.sub.2 (z) from the noise source 46 and the secondary sound sources 24.sub.1 and 24.sub.2 to the control point P. In the coefficient calculating part 45 the transfer functions C.sub.1 (z) and C.sub.2 (z) of the filters 48.sub.1 and 48.sub.2 which satisfy Eq. (14) are calculated from the acoustic transmission characteristics H.sub.0 (z), H.sub.1 (z) and H.sub.2 (z) and the transfer functions are set in the filters 48.sub.1 and 48.sub.2.
As mentioned above, the active noise controller calls for the simulation of the transmission characteristics H.sub.1 (z) and H.sub.2 (z) to obtain the filter coefficients C.sub.1 (z) and C.sub.2 (z) which are necessary for removing noise. This method is, however, defective in that the computational load for obtaining the filter coefficients C.sub.1 (z) and C.sub.2 (z) which satisfy Eq. (14) increases in proportion to the squares of the orders of the pre-measured and simulated transmission characteristics H.sub.1 (z) and H.sub.2 (z).